An operational approach to quantum probability
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GPT provides a general structure for observables (encompassing both QPT and CPT) and describes state updates using the concept of instruments.
“GPT provides a general structure for observables (encompassing both QPT and CPT) and describes state updates using the concept of instruments, as introduced by Davies and Lewis (1970) and developed by Ozawa (1984, 1985a, 1985b, 1986, 1989, 1989).”
From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Davies and Lewis (1970)
Cites
An algebraic approach to quantum field theory
Haag, R., & Kastler, D. (1964) · Journal of Mathematical Physics · doi:10.1063/1.1704187 · Cited by 1,250 · see citing works
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The Theory of Quantum Information
Watrous, J. (2018) · doi:10.1017/9781316848142 · Cited by 1,325 · see citing works
Completely positive maps and entropy inequalities
Lindblad, G. (1975) · Communications in Mathematical Physics · doi:10.1007/bf01609396 · Cited by 666 · see citing works
Quantum measuring processes of continuous observables
Ozawa, M. (1984) · Journal of Mathematical Physics · doi:10.1063/1.526000 · Cited by 504 · see citing works
The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information
Devetak, I., & Shor, P. W. (2005) · Communications in Mathematical Physics · doi:10.1007/s00220-005-1317-6 · Cited by 445 · see citing works
Quantum Theory: Informational Foundations and Foils
(2016) · Fundamental Theories of Physics · doi:10.1007/978-94-017-7303-4 · Cited by 178 · see citing works
Optimal measurement on noisy quantum systems
Watanabe, Y., Sagawa, T., & Ueda, M. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.020401 · Cited by 80 · see citing works
Quantum theory and determinism
Vaidman, L. (2014) · Quantum Studies: Mathematics and Foundations · doi:10.1007/s40509-014-0008-4 · Cited by 65 · see citing works
Ozawa, M., & Khrennikov, A. (2021) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2020.102491 · Cited by 55 · see citing works
Coupling quantum-like cognition with the neuronal networks within generalized probability theory
Khrennikov, A., Ozawa, M., Benninger, F., & Shor, O. (2025) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2025.102923 · Cited by 17 · see citing works
“This model is based on the representation of brain neuronal network functioning within generalized probability theory (GPT) (also known as operational measurement/probability theory) [25,26,38,39,64,67,68, 72,73]; for reviews, see [45,80].”
- Authors
- Davies, E. B., & Lewis, J. T.
- Affiliations
- Massachusetts Institute of Technology (US)
- Institute for Advanced Study (US)
- ORCID
- Davies, E. B.
- Venue
- Communications in Mathematical Physics
- Published
- 1970-09
- Volume
- 17
- Issue
- 3
- Pages
- 239-260
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2042457049
- Cited by
- 888
- References
- 1
- Citations by year
- 2026: 20 · 2025: 33 · 2024: 32 · 2023: 39 · 2022: 34 · 2021: 37 · 2020: 27 · 2019: 21 · 2018: 34 · 2017: 33 · 2016: 39 · 2015: 42 · 2014: 27 · 2013: 32 · 2012: 28
- FWCI
- 6.21
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Communications in Mathematical Physics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- quantum probability, quantum measurement theory, instruments, joint probability, conditional probability, repeatability, quantum operations, axiomatic quantum mechanics, repeated measures
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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